Fracture times

Equation (8.46) applies to the motion until fracture is complete. After this the form of (8.45) applies. Kipp and Grady (1985) have shown that the time to fracture (time from inception to completion of failure at the fracture zone) depends on the material and kinematic properties of the problem according to... 

Figure 6.61 Delayed fracture times and minimum stress for cracking of 0.4% C steel for various hydrogen concentrations obtained by different baking times at 150°C of cathodically charged specimens (Craig)5...

We expect that when craze sources are plentiful, resulting in a high active craze front length Q, the craze velocity that needs to be maintained to match the imposed strain rate can be proportionally lower resulting in a lower craze flow stress and an increased craze fracture time tf. The contrary will hold when craze sources are few, requiring high velocities and high craze flow stresses to be maintained. There is very little information available currently on the important dependence of the craze fracture time tf on the applied stress implied by Eq. (9). 

Compared to other methods used to extract the bending force from impact tests, it can be noted that using the present approach several drawbacks existing with the other methodologies are removed a) the increase of fracture time and addition of nonlinearities characteristic of mechanical damping b) the lack of foundation of methods used to numerically smooth the experimental registers c) the additional cost incurred when samples are instrumented. 

Intermediate Response. Figure 6 is a double logarithmic plot of o/e vs. time in seconds at three different strain rates for the samples as a function of H O content. To extend the time scale and to correlate results at various , we have used the reduced-variables procedure shown to be applicable in describing the viscoelastic response of rubbery materials (8) as well as of several glassy polymers (6). (To compensate for the effect of different e we plot a/e vs. e/e the latter is simply the time, t.) Superposition over the entire time scale for 0% H2O (upper curve) is excellent except for times close to the fracture times of the materials tested e higher strain rates. For example, a deviat ipn occurs at 10 sec for the material at e = 3.3 x 10 sec... 

Figure 9.53 shows fracture time of AISI 4340 steel baked at 150 °C for various times after initial cathodic charging [208]. After cathodic charging, DO escapes after heating at 150 °C. The incubation time, as shown in Fig. 9.53, before cracking decreases with... 

A unique feature of the fracture behavior of such polymers is its thermally assisted character as shown in Fig. 12.21 that gives the stress dependenee of the fracture time at temperatures of 153 K, 198 K, and 293 K for Nylon-6. The dependence shown in Fig. 12.21 has the signature of a kinetic process having the form of... 

Figure 8.12. Delayed fracture times and minimum stress for cracking of 0.4% C steel as a function of hydrogen content. Specimen initially charged cathodically, baked at 150°C for varying times to reduce hydrogen content [59]. [Figure 5 from H. Johnson, J. Morlet, and A. Troiano, Hydrogen, crack initiation, and delayed failure in steel, Trans. AIME 212, 531 (1958).]...

This relation is useful for industrial applications, when one knows the constants, m and C, of a material, since the above expression evaluates the fracture time on... 

It is interesting to note that according to the investigation by Kuksenko (1987), the fracture time ti is proportional to the sample sizes ranging from the order of cms to that of kms (Fig. 4). 

The average time to, until a complete extraction of the molecules with an average anchoring distance has occurred, is then proportional to the fracture time ts. An integration of Eq. 5.45 yields ... 

Upon the transformation from exponent notation back to decimal logarithm, one observes a linear decay, that is, log tf,= a- bo, where a = (l/2.3)[/o/kT + log Tq, and the coefficient b includes the reciprocal of temperature, b = (l/2.3)y/kT At very high values of stress, o UJy, the fracture time reduces to the period of oscillations in the lattice, Tq. This extrapolation does not realistically apply to the experimental data but helps one in illustrating an important point. In particular, in the log tf, plots at different temperatures, this dependence corresponds to a family of curves that converge to the pole with coordinates o = t/o/y and log t, = log Tq. The higher the temperature, the lower the position of the curves, that is, the lower the durability. 

A more interesting case is that of extrapolation to small loads. Zhurkov s formula predicts a finite fracture time at each particular temperature at o 0. This extrapolation has also been the subject of numerous debates. The experimental data show a steep increase in the fracture time when the stress is lowered to a particular value, referred as the long-term breaking point. 

As it is known [12], the elasticity modulus E value in polymiers impact tests grows at testing temporal scale decrease (at brittle fracture - time up to failure and can be described according to the empirical relationship [12] ... 

So with a wide distribution of pore size, a wide distribution of catalyst structure fracturing time is expected. But using the known pore size distribution, it can be calculated that almost all pores are filled early in the acceleration period. So this explanation must be discarded for our present problem. 

The brittle fracture of olefin polymers appears under load on a very short timescale. Brittle fracture time characterizes the mechanical behavior of a polymer, as brittleness temperature also does. 

The longest tests carried out up to failure demonstrate an acceleration of damage mechanisms during long-term tests, particularly at high temperature (Fig. 6.19(a)). In particular, a test at 600°C stiU in progress and now well into the tertiary stage wUl end after an estimated fracture time of the order of 230,000 h (Fig. 6.6(a)). This is four times less... 

Fig. 15.16 Schematic of dependency of incubation time and fracture time under static loads...

Specimen Thermal conductivity (kcal/mhK) Thermal expansion (10- /K) Elastic modulus (kg/mm ) Tensile strength (kg/mm ) Pore size (lim) Heat flux (kW/cm ) Fracture time (S) W (kW/cm" )... 

The delayed failure curves for precracked specimens of hydrogenated and Cd plated (a) AISI 4340 steel without rare earths, (b) with 0.03% Ce, (c) with 0.09 and 0.17 w/o Ce, (d) with 0.08 and 0.16 w/o La are shown in fig. 18a-d. The Ce and La additions showed a dramatic improvement in the delayed failure of 4340 steel both in fracture times and lower critical stress intensity. The lower critical stress intensity represents a three-fold... 

Fracture studies of highly oriented nylon 6 flbers were performed by Zhurkov and coworkers [27-29]. They found that the stress dependence of the fracture time exhibits characteristics of a kinetic process. The extrapolated stress data at different... 

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